Foot Length/Height Experiment

Alg II Names

Foot Length/Height Experiment Names 1) Get in groups. 2) Materials needed: a) Paper & pencil b) Graph paper c) Yardstick & ruler d) Height measuring tape e) TI-84 graphing calculator 3) Measure the foot length and height (both in inches) of each person in your group. Share your data with other groups, and use data from other groups until your group has 10 sets of data.

Foot Height Foot Height Length Length

4) Using your foot length as your domain and height as your range, organize your data in ordered pairs:

5) On graph paper, plot your ordered pairs: a) Label the x-axis as “Foot length” and the y-axis as “Height”. b) Determine the appropriate scale for each axis so that your points fit on your coordinate plane while using the entire sheet of graph paper. c) Plot the points. 6) Looking at your scatter plot, draw a general conclusion about the relationship between foot length and height. General conclusion: Circle one a) Strong Positive Correlation, b) Weak Positive Correlation, c) No Correlation, d) Weak Negative Correlation, e) Strong Negative Correlation 7) Looking at the Scatter Plot, draw a Trend line. 8) Looking at your graph, use 1 of 2 procedures to find the slope and y-intercept of your Trend Line. Show work: a) Count the ratio of rise to run. Extend your line to find the y-intercept. b) List two points on the line . Use the slope formula. Use point-slope form, and then convert to slope-intercept form. Slope = What is the y-intercept? y-intercept = Now it is time to use our Graphing Calculators to do the same work, plus some more. Foot Length/Height Experiment p. 2

1) Turn on your TI-84 and clear it. Push MODE and make sure the entire left column is activated. nd 2 QUIT. Clear all of the data out of L1 and L2 ( STAT ENTER ▲ CLEAR ENTER ► ▲ CLEAR ENTER) 2) Enter Foot Length in L1 and Height in L2. 3) Clear all the equations in Y= (Y= clear each equation, 2nd QUIT). 4) Set up STAT PLOT. (This will plot your statistics (ordered pairs) on a coordinate plane.) 2nd STAT PLOT 4 ENTER turns off all Plots. 2nd STAT PLOT 1 ENTER turns on Plot 1. ▼ ENTER sets up a scatter plot for plotting your ordered pairs on a coordinate plane. ▼ ENTER ▼ ENTER makes L1 your domain and L2 your range. ▼ and choose your marking for your scatter plot by using the arrows ENTER 2nd STAT PLOT will display that Plot 1 is on, the type of graph that will be used, the source of the data, and the type of mark that will be used. 5) ZOOM 9 will display your scatter plot on the coordinate plane. It should resemble your graph paper. 6) If you push TRACE and then arrow left or right, you will move from point to point on your scatter plot and the coordinates of each point will be listed on the bottom of the graph as you trace. Choose the two points that a Trend line would approximately pass through.

List the 2 points: Use these two points to write the point-slope form of the line. Convert to slope-intercept form. Show work:

Slope-intercept form of the Trend line in Y1 ___

7) Put that equation in Y1 and graph ( Y= enter equation ENTER GRAPH ). 8) What is the slope-intercept form of the trend line on the graph paper (see bottom of page 1)?

______

Using the values of the slopes & y-intercepts, how does line Y1 compare to the line on your graph paper? Comment: Foot Length/Height Experiment p.3 9) Now we will have the graphing calculator find our “Best Fit Line” by following the linear regression procedure:

a) STAT ► 4 L1 , L2 ENTER What are your values for a & b? a= b=

b)What is the value of r? What percentage of a perfect correlation is this? c) Put the above info into Y2=. Y= ▼ VARS 5 ► ► 1

Slope of Y2: y-intercept of Y2: Put the slope over 1. What does the slope (ratio of change of height to change of foot length) of the line in Y2 tell you about the relationship between foot length & height? Be specific:

d)GRAPH to see our coordinate plane. Compare the lines in Yand Y (refer to slope & y- intercept):

The line in Y is most accurate. Using slope & y-intercept, on a scale of 1-10, rate the line on your graph paper compared to the line in Y.

The line in Y gives us a model to predict height based on foot length. What does the y-intercept tell us about height when the foot length is zero? This answer should make sense mathematically. It does not make sense in real life. Explain:

10) Clear Y. For the following questions, use the model developed in Y to make some predictions. 2nd QUIT Go to 2nd TABLE and arrow to the appropriate value to make your predictions. Round your answer to the nearest ½ inch. a) Fred is your age and his feet are 9” long. How tall should he be? b) Basketball coaches often say, “Just wait until he/she grows into those feet!” Billy is a 7th- grader with 12” in feet. Predict how tall he will be when he is your age if, 1) His feet don’t grow: 2) His feet grow 2 inches: 3) On foot grows 3 inches, and sadly, he loses his toes from the other foot in a lawn mower accident: c) Shaquille O’Neal was 7 feet tall when he was your age. Estimate how long his feet were:

11) Comment on how you think this project could arrive at more accurate results (consider data, including data gathering, and factors that might have to do with the differences in people’s foot length as it is related to their height). Brainstorm with your group members and think critically: